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Mom time. It'd be wonderful if you could get away for a day or so to recoup. If that's impossible, try escaping with a good book or long walks as often as you can. I'll keep you in my thoughts and prayers.
Blessings
https://www.dailystrength.org/group/alcoholism
https://www.dailystrength.org/categories/Childrens_Health_Parenting
The thing that comes out the loudest from your post, is the safety of a 4-month old. As mentioned, she could have lost her life as you lay beside her in a black-out, ... not to mention her safety at any given time you are under the influence.
The question is ... what to do about it. Well, FIRST ... NEVER again put her in any danger. NEVER. Child endangerment can land you in jail ... not to mention the tragedy of any harm to her. THIS MUST STOP.
I cannot do anything about the fighting. I believe you that you are under too much demand though I find it difficult ...in that there is only you, husband, and infant in the household.
I think it best you inform your doctor of what you have posted. You need some guidance on mothering an infant and husband needs some also ... you up at 11PM fixing his dinner is not conducive to parenting an infant. SHE needs your attention more than anyone else .. and you have to be RESTED, SOBER, and in a good mindset to give it to her.
EVERYONE has to put her FIRST ... and that comes down to you and your husband ... at least. Get this fixed ... one way or another.